Gökova Geometry Topology Institute

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**Date:** September 27-28, 2021

**Speakers:** Selman Akbulut (GGTI) and Eylem Zeliha Yildiz (Duke University)

**Title:** Shaking Knots

**Abstract:** 
"Knot Shaking" is a technique introduced $44$ years ago as a tool to study exotic smoothings of $4$-manifolds with boundary. Let be $K$ be a knot, and  $K^{r}$ be the $4$-manifold obtained by attaching a $2$-handle to $B^{4}$ along $K$ with framing $r$. We say that $K$ is  $r$-shake slice if a generator of  $H_{2}(K^{r})=Z$ is represented by a smoothly imbedded $2$-sphere; this is equivalent to saying that the link consisting of $K$ and an even number of oppositely oriented parallel copies of $K$ (parallel with respect to $r$-framing) to bound disk with holes in $B^4$. Clearly slice knots are $r$-shake slice. It is known that when $r\neq 0$ not all $r$-shake slice knots are slice, and there are knots that are not $r$-shake slice. We address the important remaining case of $r=0$, and prove that $0$-shake slice knots are slice. Along the way, we discuss how shaking is related to the exotic smooth structures and corks.


**Lecture 1.** Monday, September 27 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

 By **Eylem Zeliha Yildiz**

**Zoom Meeting ID** 937 1654 5820

**Password** Initials of the speaker's name (use capitals)

** Şifre** Konuşmacının adının baş harfleri (büyük harflerle)

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**Lecture 2.** Tuesday, September 28 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

 By **Selman Akbulut**

  * [[https://www.youtube.com/watch?v=EUQNUdSctts|Lecture Video]]  

**Zoom Meeting ID** 912 1482 3818

**Password** Initials of the speaker's name (use capitals)

** Şifre** Konuşmacının adının baş harfleri (büyük harflerle)

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Gökova Geometry Topology Institute

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